The ludic numbers are obtained to a sieving process similar to the sieve of Eratosthenes, but with the imporant difference that crossed off numbers lose their positional attributes and change the positional attributes of the larger remaining numbers.

In the sieve of Eratosthenes implemented in its simplest form, without any optimization, some numbers may be crossed off more than once. For example, 6, 12, 18, 24, 36, 48, 54, ... (A033845) can be crossed off twice each (first for 2, then for 3); whereas with modest optimization, the algorithm skips 6 when it gets to 3, proceeding instead to 9 (the square of 3). But regardless of how many times a number is crossed off, the position of later numbers does not change.

With the ludic numbers, crossed off numbers are completely removed prior to the next step.

A. Write a range of integers in order into an array, starting with 1.

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

61

62

63

64

65

66

67

68

69

70

71

72

73

74

75

76

77

78

79

80

81

82

83

84

85

86

87

88

89

90

B. Start with p=2{\displaystyle \scriptstyle p\,=\,2\,}.

C. Circle or highlight p{\displaystyle \scriptstyle p\,} and cross out its square p2{\displaystyle \scriptstyle p^{2}\,} and all its higher multiples that haven't already been crossed off.